It really depends on if Edwards runs to the left on abortion during the primaries.
The most sensible position would be: "I support a 20-week ban, and a continuation of whatever laws are currently on the books, including the Hyde Amendment, but nothing further."
He would be eaten alive for supporting any abortion ban. Not that he was going to win the primary in the first place, but still.
This. Could he win the general? Yes. Could he make it there? No. If he somehow did, I'd be curious if an independent far left candidate could win a lot of votes (or the Green Party candidate). Two fairly moderate southern white guys wouldn't exactly enthuse the democrat base.